Wideband enhancement of infrared absorption in a direct pyramids

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Wideband enhancement of infrared absorption in a direct
band-gap semiconductor by using nonabsorptive
pyramids
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Citation
Dai, Weitao, Daniel Yap, and Gang Chen. “Wideband
Enhancement of Infrared Absorption in a Direct Band-gap
Semiconductor by Using Nonabsorptive Pyramids.” Optics
Express 20.S4 (2012): A519. © 2012 OSA
As Published
http://dx.doi.org/10.1364/OE.20.00A519
Publisher
Optical Society of America
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Final published version
Accessed
Thu May 26 08:52:34 EDT 2016
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http://hdl.handle.net/1721.1/78279
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Detailed Terms
Wideband enhancement of infrared
absorption in a direct band-gap
semiconductor by using nonabsorptive
pyramids
Weitao Dai,1 Daniel Yap,2 and Gang Chen1,∗
1 Department
of Mechanical Engineering, Massachusetts Institute of Technology,
77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
2 HRL Laboratories, LLC. 3011 Malibu Canyon Road, Malibu, California 90265, USA
∗ [email protected]
Abstract:
Efficient trapping of the light in a photon absorber or a
photodetector can improve its performance and reduce its cost. In this paper
we investigate two designs for light-trapping in application to infrared
absorption. Our numerical simulations demonstrate that nonabsorptive
pyramids either located on top of an absorbing film or having embedded
absorbing rods can efficiently enhance the absorption in the absorbing
material. A spectrally averaged absorptance of 83% is achieved compared
to an average absorptance of 28% for the optimized multilayer structure that
has the same amount of absorbing material. This enhancement is explained
by the coupled-mode theory. Similar designs can also be applied to solar
cells.
© 2012 Optical Society of America
OCIS codes: (040.0040) Detectors; (350.4238) Nanophotonics and photonic crystals.
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Light-trapping is essential for solar cells and photodetectors. For solar cells, light-trapping reduces the required amount of the photovoltaic materials, which brings down the cost [1] and
improves carrier collection [2]. Much effort has been devoted into designing effective lighttrapping structures for solar cells. Some general design strategies include anti-reflection structures at the top, random [3] or periodic [4–6] structures at the surfaces of the absorbing material
to scatter light, highly localized fields excited using surface plasmons [6, 7], and formation of
the absorbing material into nanostructures [8–13]. For thin-film semiconductor photodetectors,
a reduction of the volume of absorbing material that is enabled by light trapping also serves
to improve the signal to noise ratio [14]. Compared to intensive research of light trapping in
silicon photovoltaic cells, for which the material absorption can be quite low, less research
has been devoted to broadband light-trapping in photodetectors or photovoltaic cells that have
direct-bandgap absorbing material [15–18].
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In this paper we report on our investigation of light-trapping structures for infrared photodetectors working in the wavelength range from 1μ m to 5μ m. Simulations were performed with
the finite-difference time-domain (FDTD) method [19], using a freely available software package [20]. Given the objects’ geometries in the simulation area and their material properties, the
simulation software package uses Maxwell’s equations and determines the electric and magnetic field distributions. Absorption spectra and other electromagnetic variables can be further
calculated based on these field distributions. The absorption of light by a material can be determined from the imaginary part of the permittivity of the material. The relative permittivity εa
of the active material in our structure is described by the summation of Lorentzian functions:
εa = ε ∞ + ∑
m
2
ω p,m
.
2 − ω 2 − iωγ
ω0,m
m
(1)
Here ω = 2π c/λ (c is the speed of light in vacuum and λ is the wavelength in vacuum). The parameters in Eq. (1) are m = 2, ε∞ = 7.14, ω0,1 = 2.29PHz, ω p,1 = 5.11PHz, γ1 = 128PHz,ω0,2 =
7.53PHz, ω p,2 = 16.8PHz, γ2 = 4.63PHz, 1PHz = 1015 Hz. The refractive index of the active
√
material is na = εa . The real part of the refractive index is around 3.5 and the imaginary part is
around 0.1. InAs has similar refractive index values [21]. Since in this work we are focusing on
the “improvement” of the absorption, the precise refractive index values are not important. The
effective thickness de f f used as a parameter of a light-trapping structure in this work is defined
as the thickness of a uniform-thickness film which contains the same amount of absorbing material as found in the light-trapping structure. Our goal is an absorber structure whose effective
thickness is much smaller than the wavelength.
The first proposed light-trapping design is a nonabsorptive pyramid array on top of an active
film, which is shown in Fig. 1(a). A surface textured with pyramids has been demonstrated
to have enhanced trapping of the incident light [10, 22–24]. It functions as a broadband antireflection layer and also scatters light efficiently to increase the optical path length in the active
material. In our design, the light-absorbing layer is quite thin and thus we use another nonabsorptive material to form the pyramids. Similar ideas were presented previously for photovoltaic
cells having a one-dimensional grating located above a thin active layer [25]. Since the photodetectors we investigated are intended to work in the infrared regime, silicon will be a good
choice for the nonabsorptive pyramids. Its refractive index is close to the real part of the refractive index of the active material, which minimizes the reflection at the interfaces between
the nonabsorptive pyramid and the regions of active material. The pyramids are arranged in
a square lattice with a lattice constant a = 3μ m. The pyramid has a square base with width
w = 3μ m and height h = 6μ m. Under the pyramid layer is the 0.3μ m-thick active layer with a
0.4μ m-thick SiO2 layer and a gold reflector in the backside. The refractive index of silicon is
set as 3.5 in the simulations.
The absorption spectrum of this structure under normal incidence is compared in Fig. 1(c)
with the absorption spectrum of an optimized multilayer structure. The multilayer structure
consists of, from top to bottom, a 1.5μ m-thick SiO2 layer, a 0.3μ m-thick active layer, a 20nmthick SiO2 layer and a gold reflector. The thicknesses of the two SiO2 layers are optimized
to achieve the highest value, which is 0.28, for its absorptance averaged over the 1 − 5μ m
wavelength range. In comparison, the pyramid structure achieves a spectrally averaged absorptance of 0.69. Furthermore, we can achieve even higher absorption by embedding absorptive
nanorods within otherwise nonabsorptive pyramids. The active nanorods in the pyramids shown
in Fig. 1(b) have a height of hrod = 6.3μ m, radius rrod = 0.4μ m and de f f = 0.3μ m. The nonabsorptive pyramid structure includes the pyramids and a 0.3μ m-thick spacer layer. The average
absorptance for this nanorods structure is 0.79.
Nanorod arrays have been studied extensively as a light-trapping scheme [8,9,12]. Nanorods
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(a)
(b)
z
z
y
y
x
(c)
x
1
Absorptance
0.8
0.6
0.4
0.2
Multilayer
Active film under pyramids
Active rods in pyramids
0
1
2
3
4
5
Wavelength(μm)
Fig. 1. (a) Light trapping structure with an active film under nonabsorptive pyramids. From
top to bottom: the nonabsorptive pyramids (transparent light blue), the active film (blue,
0.3μ m thick), the SiO2 , layer (green, 0.4μ m thick) and the gold reflector (golden). The
pyramids have lattice constant a = 3μ m and pyramid height h = 6μ m. (b) Light-trapping
structure with active rods embedded in nonabsorptive pyramids. The rods have the height
hrod = 6.3μ m, radius rrod = 0.4μ m and effective thickness de f f = 0.3μ m. (c) The absorption spectra of the two light-trapping structures illustrated in (a) and (b) along with the
absorption spectrum of an optimized multilayer structure. The multilayer structure consists
of, from top to bottom, a 1.5μ m-thick SiO2 layer, a 0.3μ m-thick active layer, a 20nm-thick
SiO2 layer and a gold reflector.
with radial p-n junctions may simultaneously provide long optical path lengths and short carrier
collection lengths [26]. Our simulations show that the addition of nonabsorptive pyramids, into
which the nanorods are embedded, will improve the absorption in the nanorods even further.
Figure 2 compares the absorption spectra of the nanorods with and without the pyramids. The
average absorptance drops from 0.79 to 0.58 when the nonabsorptive pyramids are removed.
In Fig. 3, we plot the reflection spectra from the front surface of the active rod structure with
or without nonabsorptive pyramids. Both structures exhibit excellent broadband antireflection
properties. Though less reflection from the front surface is an important reason for the absorption enhancement over the multilayer structure shown in Fig. 1(c), we cannot use it to explain
the absorption difference shown in Fig. 2. To explain this difference in absorption, we have to
consider the interaction between the incident electromagnetic wave and these three dimensional
structures. Coupled-mode theory [27, 28] allows us to characterize a complex optical system in
the wave optics regime using just a few parameters.
The coupled-mode theory describes the interactions between the incident light and the structure as the excitation and extinction of resonant modes within the structure. The absorption
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1
Absorptacnce
0.8
0.6
0.4
0.2
Active rods in pyramids
Active rods in air
0
1
2
3
4
5
Wavelength(μm)
Fig. 2. Absorption spectra of active rod structures with nonabsorptive pyramids, as shown
in Fig. 1(b), and without the nonabsorptive pyramids. The inset shows an illustration of
structure with the active rods in air, without any nonabsorptive pyramids
0.02
Bottomless pyramid
Infinitely long rod
Reflectance
0.015
0.01
0.005
0
1
2
3
4
5
Wavelength(μm)
Fig. 3. Reflectance spectra of the bottomless pyramid structure and the infinitely long rod
structure. The bottomless pyramid structure has the same parameters as the structure shown
in Fig. 1(b) except the nonabsorptive pyramids and the active rods extend to infinity in the
−z direction. The infinitely long rod structure is a bottomless pyramid structure for which
the nonabsorptive pyramids are replaced by air.
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2000
0.8
Absorptance
1
2000
1500
0.6
0.8
1500
0.6
1000
0.4
1000
0.4
500
0.2
0
4
4.2
4.4
4.6
4.8
0
5
500
0.2
0
3.7
Wavelength(μm)
3.9
4.1
4.3
4.5
4.7
4.9
Normalized Stored Energy
(b)
1
Absorptance
Normalized Stored Energy
(a)
0
Wavelength(μm)
Fig. 4. (a) Absorption spectra of the light-trapping structures shown in Fig. 1(a) (red curve
with circles) and 1(b) (blue curve with squares), along with the spectral distribution of
the energy stored in a pyramid structure that doesn’t have any active material. The stored
energy is normalized by the electromagnetic energy carried by the incident plane wave
in the same volume of free space. (b) Absorption spectrum of the light-trapping structures
shown as the inset of Fig. 2, along with the spectral distribution of normalized energy stored
in that rod structure when the rod is lossless.
spectrum contributed by one resonant mode is [29, 30]
A(ω ) =
γi γe,0
.
(ω − ω0 )2 + (γi + ∑m γe,m )2 /4
(2)
Here ω0 is the resonant frequency. γi and γe,m describe how energy leaves the excited mode: γi is
internal energy loss rate through absorption by the active material within the structure and γe,m
is the external energy loss rate from having the light coupled out of the structure. This light is
seen as being reflected or back-scattered by the structure. The subscript m means there are several out-coupling channels. γe,0 (with m = 0) also describes the energy injection or in-coupling
rate from the incident light into that resonant mode. The absorption spectrum has a peak at the
resonance wavelength of the mode. Many modes exist in this structure. Therefore, the final absorption spectrum is the summation of the contributions from each of those modes. Generally
speaking, more excited modes results in higher spectrum-integrated absorption. Higher refractive index materials support more modes. For example the density of states is proportional to
n3 for bulk materials [31]. So replacing air with silicon will increase the number of modes significantly. We can see in Fig. 2 that the absorption spectrum of the structure with active rods in
high-index pyramids has many more peaks than the spectrum of the structure with active rods
in air.
Another important feather of Fig. 1(c) is that the peaks of the absorption spectra of the two
structures shown in Fig. 1(a) and 1(b) are always located at the same wavelengths. Figure 4(a)
plots the details of the two spectra for the wavelengths between 4μ m and 5μ m along with the
energy stored in a pyramid structure of the same dimensions that does not contain any active
material. Based on the coupled-mode theory, the energy stored in a mode of the passive structure
is
γe,0
.
(3)
Energy ∝
2
(ω − ω0 ) + (∑m γe,m )2 /4
γi = 0 here because no absorbing material exists. If we can assume that γe,m is not affected
significantly by the presence and locations of the absorbing material in the pyramidal structure,
the stored energy spectrum should have the same peak wavelengths and have narrower peak
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2000
Absorptance
0.8
1500
0.6
1000
0.4
500
0.2
0
4.4
4.45
4.5
4.55
Normalized Stored Energy
1
0
4.6
Wavelength(μm)
Fig. 5. Absorption spectra of a low loss pyramid structure (red curve with circles) and a
structure with low loss absorbing rods embedded in nonabsorptive pyramids (blue curve
with squares), along with the spectral distribution of the energy stored in a pyramid structure that doesn’t have any active material. The permittivity of the active material in the
low loss pyramid structure is 12.25 + 0.01i; the permittivity of the active material in the
low loss rod structure is 12.25 + 0.1i. Originally the permittivity of the active material is
around 12.2 + 0.65i.
widths compared with the absorption spectra. The simulation results shown in Fig. 4(a) indeed
confirm this behavior. A similar analysis was done for the structure with active rods in air
(without the nonabsorptive pyramids) and the results are shown in Fig. 4(b). Obviously the
two closely spaced modes with resonant wavelength near 3.9μ m are responsible for the broad
absorption peak around 3.9μ m. These results show that the many resonant modes supported
by the high-index pyramids do improve the spectrally integrated absorption that occurs in the
small active volume of the light-trapping pyramidal structures.
The only anomaly is the very high peak at 4.49μ m evident in the stored energy spectrum
shown in Fig. 4(a). Note that the absorption spectra do not show a corresponding peak at this
wavelength. This peak in the stored energy spectrum is very narrow, which suggests that for
the associated mode, ∑m γe,m are small based on Eq. (3). In addition, if γi ∑m γe,m , the contribution from this mode to the absorption spectrum will be small based on Eq. (2). Note γe,0
is one of γe,m . When ∑m γe,m is small, γe,0 also is small. However, if the value for γi is even
smaller, we can observe a distinct absorptive peak around 4.49μ m. We show in Fig. 5 the absorptance spectrum obtained for a structure for which the whole pyramid is absorptive but the
value for the imaginary part of the relative permittivity of the active material is only 0.01 compared to a value of 0.65 for the active material in the structure of Fig. 4(a). In this case, there
is a pronounced peak at 4.49μ m in the absorption spectrum. Likewise, Fig. 5 also shows the
absorptance spectrum of a structure with an active but lower loss rod. The active material in
that rod has a value of only 0.1 for the imaginary part of its relative permittivity. Again, the
absorptance spectrum has a distinct peak at 4.49μ m.
Additional insight can be provided by considering the optical-field distributions of the light in
these structures. These field distributions are a superposition of the distributions for the different
modes excited simultaneously in the structure. Figure 6 shows the electric-field energy density
distributions obtained at the wavelength of 4.510μ m for five different cases. In Fig. 6(a), the
entire pyramid is lossless. In Fig. 6(b), the entire pyramid consists of a low loss active material.
In Fig. 6(c), the structure has a low-loss active rod embedded in each otherwise transparent
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Fig. 6. Electric-field energy density distributions along two cross sections of a pyramid
when the wavelength of the light is 4.510μ m. (a) The entire pyramid is lossless; (b) The
entire pyramids consists of a low loss material with εa = 12.25 + 0.01i; (c) The structure
has a low loss active rod with εa = 12.25 + 0.1i embedded in each otherwise transparent
pyramid; (d) The structure has an active rod with εa = 12.2 + 0.65i embedded in each otherwise transparent; (e) The structure has an active film with εa = 12.2 + 0.65i under transparent pyramids. The maximum value for the electric-field energy density shown in each
figure (dark red region) is (a) 3.7 × 10−9 J/m3 ; (b) 2.4 × 10−9 J/m3 ; (c) 2.3 × 10−9 J/m3 ;
(d) 6.0 × 10−10 J/m3 ; (e) 5.5 × 10−10 J/m3 . The electric-field of the incident plane wave
has a magnitude of 1V/m.
pyramid. In Fig. 6(d), the structure has a higher loss active rod embedded in that pyramid.
And, in Fig. 6(e), the structure has a transparent pyramid and a thin film of the higher loss
active material located underneath the pyramid. We can see that the optical field distributions
are similar to each other for all of these cases, which suggests that the same mode is excited
by the incident light at this wavelength, although the intensity of the mode is weaker when
the absorption is strong. Incidentally, the absorption spectra in Fig. 4(a) and Fig. 5 all show
distinct peaks at 4.51μ m. Also, the stored energy spectrum has a weak and broad peak at this
wavelength, which suggests that ∑m γe,m , and likely γe,0 , is fairly large for this mode. As the
loss of the active regions in the structure increases, one would then expect the absorptance peak
at 4.510μ m to become higher and higher, as observed from a comparison of Fig. 4(a) and Fig.
5.
For comparison, Fig. 7 shows the electric-field energy density distributions obtained at the
wavelength of 4.488μ m for these same five cases. We can see that the optical field distributions
are similar to each other for the first three of these cases, which again suggests that the same
mode is excited by the incident light at this wavelength. However, in Fig. 7(d) and Fig. 7(e),
the electric-field energy density distributions obtained for the structure containing the higher
loss active material are quite different from the electric-field energy density distributions obtained for the lossless pyramid. Thus, other modes are dominant in these latter two cases. In
the absorption spectra for these latter two cases, which are shown in Fig. 4(a), there is significant absorptance at 4.488μ m. But the even greater absorption of the nearby absorption peak
at 4.510μ m dominates the spectrum. In contrast, for the cases with low-loss absorbing regions,
whose absorption spectra are shown in Fig. 5, the peak at 4.488μ m is distinct from the weaker
peak at 4.510μ m.
The discussions above illustrate that the presence of the active material in a structure, when
that active material has the same real part of the refractive index as the material of the nonabsorptive pyramids, will not change the resonance wavelengths. However, it can influence the
absorption rate γi of various modes. We can thus fine tune the absorption spectrum by changing
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Fig. 7. Electric-field energy density distributions for the same five cases as Fig. 6 when
the wavelength of the light is 4.488μ m. The maximum value for the electric-field energy
density in each figure is (a) 2.3 × 10−8 J/m3 ; (b) 6.1 × 10−9 J/m3 ; (c) 4.3 × 10−9 J/m3 ; (d)
6.8 × 10−10 J/m3 ; (e) 6.4 × 10−10 J/m3 .
the location and the shape of the active material. Such fine tuning is also evident when one
compares the two absorption spectra shown in Fig. 4(a).
We now consider the effect of the shape and location of the active material on the value
achieved for the spectrally averaged absorptance. Figure 8 shows the average absorptance of
active rods within nonabsorptive pyramids when the height of the active rods hrod changes
from 6.3μ m to 0.3μ m. The radius of the rods changes with the height to keep de f f = 0.3μ m.
When hrod = 0.3μ m, the rods become a thin film. The structure with rods hrod = 4μ m has the
maximum average absorptance 0.83. Generally speaking the average absorptance of a structure
with pyramids remains high regardless of the shape of the active material within it, as compared with the average absorptance of a structure with absorbing rods that are not embedded in
pyramids. The reason is because the nonabsorptive pyramids support many resonant modes in
the broad wavelength range. There will always be some resonant modes which can contribute
to the absorption spectrum significantly no matter where the active material is located.
The shape of the nonabsorptive pyramids will also influence the absorption. When the lattice
constant is too small (a < 2μ m), the pyramids cannot scatter long wavelength light efficiently.
So the absorption in the long wavelength regime becomes weak [10]. When the lattice constant
changes from 3μ m to 5μ m with the pyramid height fixed at 6μ m, our simulations show the
average absorptance in the thin film structure remains the same and the average absorptance in
the rod structure with hrod = 6.3μ m decreases from 0.79 to 0.73. The main difference in their
absorption characteristics appears in the short wavelength regime. In this regime we can treat
the light as rays. When the lattice constant is larger, these rods become more sparsely distributed. More rays are reflected back without hitting the rods and the absorptance decreases. The
pyramid height h also influences the absorption. The pyramids serve as a better anti-reflection
layer when h increases. But the incremental improvement is small when h > 6μ m. In general,
the nonabsorptive pyramids do enhance the absorption in the active material regardless of the
specific shapes of those pyramids, although the values for the average absorptance obtained
with each shape may be different.
Finding low-cost materials that have both a high refractive index and low loss in the visible
regime is a significant challenge. If we want to extend the photodetectors’ wavelength range
into the visible regime or design similar structures for solar cells, we should also consider
nonabsorptive pyramids that have a lower refractive index. Figure 9 shows how the absorption
changes with the refractive index of the pyramids n p . When the active material is a thin film,
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Received 30 Mar 2012; revised 25 May 2012; accepted 25 May 2012; published 15 Jun 2012
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Average absorptance
1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
6
7
Rod height(μm)
Fig. 8. Average absorptance for the wavelength range from 1μ m to 5μ m vs. the height of
the active rods in the nonabsorptive pyramids. The red line with circles shows the average
absorptance of active rods within nonabsorptive pyramids having n p = 3.5. The blue line
with squares shows active rods in air. The six insets show the cross section illustration of
structures with or without the nonabsorptive pyramids, for values of hrod = 0.3μ m, 3μ m
or 6.3μ m All of the structures have the same effective thickness de f f = 0.3μ m. Note that
when hrod = 0.3μ m, the rod becomes a laterally continuous film.
Average absorptance
1
0.8
0.6
0.4
0.2
0
1
1.5
2
2.5
3
3.5
Refractive index
Fig. 9. Average absorptance for the wavelength range from 1μ m to 5μ m vs. the refractive
index of the nonabsorptive pyramids. The red curve with circles represents the absorption
in the structure having a 0.3μ m-thick film; the blue curve with squares represents the absorption in the structure having active rods with hrod = 3μ m and de f f = 0.3μ m.
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Received 30 Mar 2012; revised 25 May 2012; accepted 25 May 2012; published 15 Jun 2012
2 July 2012 / Vol. 20, No. S4 / OPTICS EXPRESS A528
1
Average Absorptance
n p = 1.5
n p = 3.5
0.9
0.8
0.7
0.6
n p = 3.5
0.5
0
10
np = 1
20
30
40
50
60
Incident angle(degree)
Fig. 10. Average absorptance for incident light in the wavelength range from 1μ m to 5μ m
under oblique incidence angles. Four structures are studied that have: the 0.3μ m-thick active film under the nonabsorptive pyramids with n p = 3.5 (black); the active rods with
hrod = 3μ m and de f f = 0.3μ m in the nonabsorptive pyramids with n p = 3.5 (magenta), or
with n p = 1.5 (blue); and the same rods in air (red). The circles represent s polarization and
the crosses represent p polarization.
the average absorptance increases almost linearly with an increase in n p . But for the structures
having active rods embedded in the pyramids with hrod = 3μ m, the average absorption increases
quickly for small n p and begins to saturate at a maximum value when n p reaches 1.5. This
means we have various choices of materials for constructing the transparent pyramids.
We also studied the angular and polarization dependence of the absorption. The results are
shown in Fig. 10. Four designs were studied: a structure with a 0.3μ m-thick active film under
the nonabsorptive pyramids with n p = 3.5; and structures with active rods with hrod = 3μ m and
de f f = 0.3μ m in nonabsorptive pyramids whose refractive index is n p = 3.5, n p = 1.5 or n p = 1.
The incident plane is the x − z plane shown in Fig. 1(a) and Fig. 1(b). Both s polarization and p
polarization are simulated. At incidence angles up to 60◦ , the values for the average absorptance
of all four designs remain high. Figure 10 shows clearly that the absorption is enhanced by the
nonabsorptive pyramids for a large range of the incidence angles and for both polarizations of
the light.
In the end of the paper we briefly address the pyramid fabrication. The nanorod rod array
can be made by photolithography and etching, or other methods. If a polymer material is used
to form the pyramids, we can fabricate these pyramids by depositing the polymer film and
then use direct laser writing [32] or soft lithography techniques [18, 33] to define the pyramid
shape. Depositing a high-index silicon or III-V semiconductor film on top of the nanorod array
followed by some lithography method and etching can yield high-index pyramids.
In conclusion we presented two light-trapping designs: an active film under nonabsorptive
pyramids and active rods embedded in nonabsorptive pyramids. Our simulations demonstrate
the significant absorption enhancement provided by the nonabsorptive pyramids. We used
coupled-mode theory to explain this enhancement. Although we design these structures for
infrared photodetectors, similar design principles can also be used for solar cells.
Acknowledgments
This work was supported by DARPA and by a DoD MURI via UIUC.
#165787 - $15.00 USD
(C) 2012 OSA
Received 30 Mar 2012; revised 25 May 2012; accepted 25 May 2012; published 15 Jun 2012
2 July 2012 / Vol. 20, No. S4 / OPTICS EXPRESS A529
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